# Talk by Patricia Alonso Ruiz

On May 15th, 2024, **Patricia Alonso Ruiz** (Texas A&M) gave a talk about **"Where could p-energies come from? On a quest to find them in Cheeger spaces"** as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

The classical p-energy is a functional that arises by integration of the pth power of the gradient. It is associated with a non-linear operator, the p-Laplacian, that serves as the basis of many problems in PDE. Being defined in terms of a gradient, one runs into trouble when the underlying space has no straightforward notion of the latter. Can we make sure that there is still a natural notion of p-energy in the absence of a gradient?

Motivated by that question, we discuss in this talk a way to construct a p-energy in the framework of Cheeger spaces without involving their differential structure. Instead, we will exploit the characteristic features of a Cheeger metric measure space: The doubling property and a (p, p)-Poincaré inequality for Lipschitz functions.

The talk is based on joint work with Fabrice Baudoin.